1. Field of the Invention
This invention relates to a method and apparatus for determining fluid-dynamic drag resistance experienced by a model in an environmental test facility, and more particularly, to a method and apparatus for determining small magnitude fluid-dynamic drag resistance differentials in an environmental test facility between a baseline model and the baseline model with a minor external structural modification superimposed thereon.
2. Description of the Prior Art
The baseline configurations of the external structures of most air and water operated vehicles have been fairly well stabilized such that the basic fluid-dynamic drag resistance characteristics of these vehicles are established. It has been noted, however, that the drag resistance characteristics of these vehicles change slightly when minor structural modifications are superimposed upon the external structure of the basic vehicle configuration. For example, a ship appendage may have different shapes or an aircraft may have different leading or trailing edge configurations of its airfoils. Other examples of possible structural modifications which affect the drag resistance characteristics of a vehicle include smoothing of exterior surfaces, changing the size, shape and/or location of control surfaces, filling in cavities and gaps, and filleting of appendage-main body intersections. A single modification superimposed upon the basic vehicle configuration, or combinations of these modifications superimposed upon the basic vehicle configuration can provide a marked reduction in drag resistance which can result in significant savings in energy consumption over the lifetime of the vehicle and a beneficial increase in the operating parameters of the vehicle.
Conventional design methodology investigates the effects of proposed structural modifications by the construction and testing of models representing the basic vehicle configuration and the basic vehicle configuration as altered by the proposed structural modifications. Inasmuch as the hereinabove delineated modifications to the basic vehicle configuration produce changes in magnitude in the fluid-dynamic drag resistance experienced by the models tested in an environmental test facility which are small in relation to the total fluid-dynamic drag resistance experienced by the models, it is difficult to determine the total drag resistance with sufficient accuracy to accurately assess the magnitude of these small changes in drag resistance effected by the hereinabove delineated structural modifications. Therefore, it is desirable to have the capability to independently determine small changes in magnitude of fluid-dynamic drag resistance in order to obtain data for inputting to various cost versus payoff studies.
Conventional model experimental methodology involves the separate measurements of the total fluid-dynamic drag resistance of a baseline model and the total fluid-dynamic drag resistance of the baseline model with the proposed structural modification, and then mathematically comparing the results to ascertain the effected change in drag resistance. The drag resistance of a model may be represented in the form: ##EQU1## and Cd is the drag coefficient, Fn is the Froude number, Rn is the Reynolds number, D is the drag resistance, q is the dynamic pressure, A is a characteristic area of the model such as wetted area or cross-sectional area, V is the free stream velocity, .nu. is the kinematic viscosity of the fluid, .rho. is the density of the fluid, and "Geometry" is the external structural configuration of the model. The models are placed in an environmental test facility and subjected to predetermined experimental operating conditions so that the total fluid-dynamic drag resistance of each model may be ascertained, and then mathematically compared to determine if the proposed structural modification is efficacious in reducing drag resistance. Methods for designing such environmental tunnel experiments are outlined in C. Lipson, N.J. Sheth, "Statistical Design and Analysis of Engineering Experiments", McGraw-Hill Book Co., New York, N.Y. (1973), and H. Schenck Jr., "Theories of Engineering Experimentation", McGraw-Hill Book Co., New York, N.Y. (1961). As long as the measured difference in drag resistance is sufficiently greater than the uncertainty in the measurements, these methods will yield statistically significant results.
Uncertainty is an estimate of the error, i.e., the difference between a measured value and the true value for a given experimental datum, which consists of a fixed, or bias, error and a random, or precision, error. Uncertainties in environmental test facility experimental data enter into the measurements and are propagated through all parameters, and these uncertainties may be calculated according to ASME standards. See S.J. Kline, F.A. McClintock, "Describing Uncertainties in Single-Sample Experiments", Mechanical Engineering, ASME (January 1953), and R. Abernathy, "Measurement Uncertainty for Fluid Flow in Closed Conduits", ASME (1982), for discussions regarding uncertainties and their effect on experimental data. The ASME standard for reporting mean data with an uncertainty band, i.e., a confidence interval, is: ##EQU2## where X is the mean value of the experimental data, U is the uncertainty, B is the bias error, t95 is the 95th percentile point for the two-tailed t-distribution which is approximately equal to two for a large number of samples, S is an estimate of the standard deviation of the population, N is the number of samples, and t95*S is the precision error expressed as the half-width of the confidence interval about the true mean. By analyzing the results of some high quality, conventional drag resistance experiments, it was determined that these types of experiments could be expected to produce statistically significant drag resistance differentials between models differing only by minor structural modifications down to only about one percent of the total fluid-dynamic drag resistance at a ninety-five percent confidence level. For additional details, see D.A. Sandell, "Statistical Design of Experiments for Submarine Speed Improvement Program", Report No. CGARD-04-77 (August 1977). For the types of structural modifications delineated hereinabove, the magnitude of the fluid-dynamic drag resistance differential between the baseline model and the baseline model with the proposed structural modification superimposed thereon is less than one percent of the total fluid-dynamic drag resistance. Hence, conventional model experimental methodology is inadequate for accurately determining the magnitude of the fluid-dynamic drag resistance differentials for the hereinabove delineated structural modifications, i.e., when the fluid-dynamic drag resistance differentials of concern are less than one percent of the total fluid-dynamic drag resistance experienced by the models, the uncertainty in the measurements of the experimental data results in fluid-dynamic drag resistance differentials which are not statistically significant. To generate fluid-dynamic drag resistance differentials which are statistically significant, conventional model experimental methodology must reduce both the precision error and the bias error. The precision error may be reduced by utilizing higher precision equipment, i.e., reducing S, and/or making more measurements, i.e., reducing t95 towards two and increasing N in the denominator of the precision error component of the uncertainty factor. This approach, however, results in increased costs due to the use of higher precision equipment and the increase in environmental test facility usage time. Furthermore, conventional model experiments require the fabrication of a multiplicity of models, the baseline model plus one baseline model for each proposed structural modification which is being considered which significantly increases the cost of conventional test facility methodology. Precision fabrication, to minimize structural deviations among models, also increases the cost of utilizing the methodology of conventional model experiments in determining small magnitude fluid-dynamic drag resistance differentials. Conventional model experimental hardware/methodology makes the reduction of bias errors to a value of less than one percent, such that fluid-dynamic drag resistance differentials of a magnitude of less than one percent of the total fluid-dynamic drag are statistically significant, improbable. It is often noted that bias errors arising from conventional model experimental methodology using the same experimental hardware under repetitive fluid flow conditions are much greater than one percent.